To setup a Ticket Category in Autotask to be as the to be use when creating Tickets from BC into Autotask.

And

Find the Tickect CatogoryID (number), so it can use in BC.

In many cases in Autotask you will se a text, then real vaul when integrate is a number like BC=100 or its different in any Autotask setup, so you have lookit up after creation.

When you say you get 100 and in the customer you get 3 are you talking about the TicketCategory ID or the number of Ticket Categories available to use in the customer database? The number of TicketCategories will differ in every customer Database. The Default TicketCategroy will be identified with the boolean field isGlobalDefault.